M4 partial — Search shipped, browse UI live on the Pi

Sidecar gains the 'search' op via rustypipe's
query().search::<VideoItem,_>() — returns id, title, channel, duration,
thumbnails, view_count. Default limit 25.

Addon root directory is no longer a placeholder notification:
- 'Search' entry → ?action=search → keyboard input → result list →
  tap a result to play (each result is a play-action plugin URL).
- 'Play by URL' entry → ?action=play_by_url → keyboard input → PlayMedia.
- ?action=search also accepts inline 'q=…' so JSON-RPC clients can
  drive search without going through the on-TV keyboard (useful for
  share-to-TV from phone + tests).
- Result labels formatted as 'Title  ·  Channel  ·  Duration  ·  Views',
  with thumbnail + Kodi InfoLabels for richer skin views.

Verified via Files.GetDirectory JSON-RPC: 19 well-formatted LTT results
returned for query 'linus tech tips'.

Pending M4: channel browse, playlist browse, pagination, search history.
Addon version 0.0.6.

sidecar/crates/torttube-sidecar/src/resolve.rs

@@ -5,6 +5,40 @@ use serde_json::Value;
 
 use crate::{run_yt_dlp, HandlerError};
 
+/// Search YouTube via rustypipe. Returns `SearchResult<VideoItem>` as JSON —
+/// the Python addon picks the fields it needs (id, name, channel, duration,
+/// thumbnail, view_count, …) to build a Kodi directory listing.
+pub(crate) async fn search(query: &str, limit: u32) -> Result<Value, HandlerError> {
+    use rustypipe::client::RustyPipe;
+    use rustypipe::model::VideoItem;
+
+    let rp = RustyPipe::new();
+    let result = rp
+        .query()
+        .search::<VideoItem, _>(query)
+        .await
+        .map_err(|e| classify_rustypipe_error(&e))?;
+
+    // SearchResult<VideoItem>.items is a Paginator<VideoItem> — take the first
+    // page truncated to `limit` items.
+    let items_json: Vec<Value> = result
+        .items
+        .items
+        .iter()
+        .take(limit as usize)
+        .filter_map(|v| serde_json::to_value(v).ok())
+        .collect();
+
+    tracing::info!(query, count = items_json.len(), "search ok via rustypipe");
+
+    Ok(serde_json::json!({
+        "source": "rustypipe",
+        "query": query,
+        "items": items_json,
+        "corrected_query": result.corrected_query,
+    }))
+}
+
 /// DASH-ready resolve: returns rustypipe's full `video_only_streams` +
 /// `audio_streams` arrays + `details`. The Python addon builds an MPD
 /// from these and hands it to inputstream.adaptive — unlocks 1080p+ via